Michelson and Stratton — New Harmonic Analyzer. 11 



The average error is only 

 0*65 of one per cent, of the 

 value of the greatest term. 



The accuracy of the result 

 is also shown in curves A and 

 B (fig. 11). The former gives 

 the summation of the calcu- 

 lated terms and the latter of 

 the observed. 



Another illustration is 

 given in figure 12 in which 



<p{x) — e~ a x 



For a~'\ the following 

 are the values of the coeffi- 

 cients of the first twelve terms 

 of the equivalent Fourier 

 series. 



12. 





p(X) 



x cos kx dx 





n. 



obs. 



calc. 



A 







100-0 



100*0 



o-o 



1 



95-0 



96-0 



-l'O 



2 



85-0 



86*0 



-1-0 



3 



70-0 



70-0 



o-o 



4 



53-0 



54-0 



-1.0 



5 



3 8 



38-0 



o-o 



6 



25-0 



25-0 



o-o 



7 



16-0 



15-0 



1-0 



8 



8'8 



8-0 



-0-8 



9 



5-0 



4-5 



0-5 



10 



3'6 



2-0 



1-6 



11 - 



2'4 



l'O 



1-4 



12 



1-6 



0-5 



1-1 



Here the average error is 

 only 0*7 percent of the value 

 of the greatest term. 



The complete cycle of op- 

 erations of finding the coeffi- 

 cients of the complete Fou- 

 rier series (sines and co- 

 sines) and their recombina- 

 tion, reproducing the origi- 

 nal function, is illustrated 

 in figure 13. A is the original curve. 





||;i|||||iiu 



ftt+ftitttff 

























-t:--4-_:= 









n 



t^rlSir 



(S 



: ^r 



ji 





::.-:- 



ffitsff 



1= FT 



: ::: 



^TFrP 



: I | B: 



- v 



- 



.... 



:. ... ... I.. 



jjfrffi if 



m& 







I^MH 



i 









\^ 



■■■ 







ill 









l 7 : 













:: - 





t "*:;".". z~.- 









:: : - 





i ±i±j -|rr: 







;.U:; : J.l : .; ! ;■:■■; 



l£l 











^iHg^ 



p 







-! 







S; 



of 



J <p{x) si 



sin lexdx and 



/* 



B and O are the values 

 °A cos kx dx respectively. Their in- 



